Fig. 5: Nonlinear vibrational coupling model vs expt.

a Experimental power-normalized SERS spectra at low (blue) and high (red) powers. Constant ERS background is estimated by dashed lines. b Corresponding theoretical results showing the SERS spectra vs CW illumination power, for 100 molecules arrayed around the gap centre. c, d Extracted Raman integrated in the region around the 1586 cm⁻¹ peak (blue line/symbols) and in the softened+background region between 1350–1500 cm⁻¹ (grey line/symbols) for theory and experiment (SERS normalized by power in d, as in Fig.4g–i). Experimental data are averages of many particles with error bars indicating standard deviation of individual measurements. In c, d, scaling of in-coupled power from theory by 0.24 is used to match with experiment. The transfer in weight from the 1586 cm⁻¹ peak to lower wavenumbers arises from the redistribution of emission to the red-shifted lowest-energy bright Raman collective mode.